Department of Statistics

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Browsing Department of Statistics by Subject "Actuarial Premiums"

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    Adopting Zero Inflated Models For Claim Counts And The Gamma Regression Model For Claims Cost In Determining Actuarial Premiums
    (University Of Ghana, 2022-04) Amenu, F.M.
    Insurance is the exchange of risk by an insured person through the payment of premiums for financial protection and economic benefit. The problem is how premiums should be charged so as to keep the industry alive to perform this basic function of insurance. Because of the Bonus-Malus system, or Hunger for Bonus system (also called No Claim Discount), and deductibles, most claims are not reported by policyholders, causing the number of claims to be dominated by zeros, which leads to over-dispersion in the data. In modeling the claim frequency, the Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models were adopted. The Gamma regression model was used to fit the claims cost data. The claim frequency regression model that best fits the claim frequency with the Gamma model for the claims cost was combined in determining the actuarial premium. These models were numerically illustrated with data obtained from a major non-life insurance company in Ghana and French Motor Third- Party Liability data from https://www.kaggle.com/datasets/karansarpal/ fremtpl2-french-motor-tpl-insurance-claims. The score test demonstrated the inability of the Poisson model to appropriately model the claims data due to the inflation of zeros in the data. The ZIP and ZINB were both found to be superior to their conventional equivalents based on the Vuong test statistics. The ZIP was chosen as an appropriate model for analyzing claim frequency data for both the French and Ghanaian data based on the values of the AIC and BIC. The risk factors that were found to influence claim frequency and claim cost were discovered to be different when both datasets were used. It is recommended that a separate analysis of claim frequency and claim cost be conducted with claim frequency receiving a high rating power.